Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
dimension and, secondly, the maximum dimensionality of a fractal is bounded by the space
that it sits in. The Koch curve is an unruly line in two-dimensional plane, and it’s thought of
as having dimension 1.26. A mountain is a messy surface in three-dimensional space, and its
dimensionality might be something like 2.1. If we had a sufficiently spiky fractal we might
actually need a higher N-dimensional space to hold it without its part having to overlap.
Speaking of mountains, the parts of a mathematical fractal need not be perfect copies
of the whole. It’s perfectly all right to have the patterns vary a bit from level to level. The
idea is that a spur on a mountain looks quite a bit like the whole mountain, even though it
isn’t an exact replica. The outcroppings on the spur in turn resemble the spur, even though
they aren’t scale models of it. The outcroppings have mountainous little bumps on them, and
the bumps have little jags, and if you get a magnifying glass you’ll find zigs and zags upon
the jags.
Among the physical forms that are commonly thought of as being like fractals are the
following. Dimensions between 1 and 2: coastlines, trees, river drainage basins. Dimensions
between 2 and 3: mountains, clouds, sponges. Fractal forms are found within the human body
as well. Among these are the circulatory system, the nervous system, the texture of the skin,
the eye’s iris, the convoluted surface of the brain, and the spongy masses of the internal
organs.
A tree is a particular kind of fractal that’s particularly important for the present
discussion. If you look closely at a tree, you’ll readily notice that it has a trunk with big
branches. There are subbranches coming off of the branches, and there are subsubbranches
upon the subbranches, and so on through five to seven levels of branching.
I used to have the mistaken idea that a tree branched by splitting the tips of its
branches, but this isn’t really the way it works. The way a tree grows is that a new branch
forms upon the smooth part of any sufficiently long piece. The basic move is like a
branchign tree.
[Show A branching tree fractal of dimension 1.46.]
You might object to my calling the oak tree in your yard a fractal, because your oak’s
branching structure does not in fact have endlessly many levels of detail (as a true
mathematical fractal would). When you get down to the twig level, the parts no longer
resemble the whole. No matter. Even though an actual physical tree has a limited number of
branching levels, it can be useful to think of it being a fractal. What we’re doing here is a
special kind of idealization in which we approximates high complexity by infinite
complexity. Oddly enough, this makes things easier. As the mathematician Stan Ulam once
said about a particular problem, “The infinite case is easy. The finite case takes too long.”
Alright, now I’m ready to state my point. Both the Web and the mental world of your
ideas are N-dimensional fractal trees.
There is a loose sense in which thinking is like moving about in a space of ideas. I
visit this notion or emotion, then that one, and then perhaps I return to the first thought. My
familiar thoughts are somewhat fixed and persistent, a bit like objects in a landscape.
Suppose that I use the word “mindscape” to stand for the manifold of possible thoughts.
There’s clearly some overlap between my mindscape and yours. It’s suggestive to
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